### Abstract

We prove a law of large numbers in terms of uniform complete convergence of independent random variables taking values in functions of 2 parameters which share similar monotonicity properties as the increments of monotone functions in the initial and the final time parameters. The assumptions for the main result are the Holder continuity on the expectations as well as moment conditions, while the sample functions may contain jumps.

Original language | English |
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Pages (from-to) | 171-192 |

Number of pages | 22 |

Journal | Journal of Mathematical Sciences (Japan) |

Volume | 25 |

Issue number | 2 |

Publication status | Published - 2018 Jan 1 |

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### Keywords

- Complete convergence
- Counting process
- Law of large numbers
- Sum of independent random processes

### ASJC Scopus subject areas

- Mathematics(all)